A ladder 18 ft long rests against a vertical wall. Let θ be the angle between the top of the ladder and the wall and let x be the distance from the bottom of the ladder to the wall. If the bottom of the ladder slides away from the wall, how fast does x change with respect to θ when θ = π 3 ?
Answers
Answer: [tex]9\ ft/rad[/tex]
Step-by-step explanation:
Given
Length of the ladder is [tex]l=18\ ft[/tex]
Angle between the wall and the ladder is [tex]\theta[/tex]
from the figure, we can write
[tex]\Rightarrow \sin \theta=\dfrac{x}{18}\\\\\Rightarrow x=18\sin \theta[/tex]
Differentiate the above equation w.r.t [tex]\theta[/tex]
[tex]\Rightarrow \dfrac{dx}{d\theta}=18\cos \theta\\\\\text{at }\theta=\dfrac{\pi }{3}\\\\\Rightarrow \dfrac{dx}{d\theta}=18\cos(\dfrac{\pi}{3})\\\\\Rightarrow \dfrac{dx}{d\theta}=18\times 0.5\\\\\Rightarrow \dfrac{dx}{d\theta}=9\ ft/rad[/tex]
Related Questions
What is the value of this number in decimal form?
Three hundred sixty-seven thousandths.
Answers
Step-by-step explanation:
the other answer is correct.
just for a little bit of explanation :
the first position after the decimal point is for tenths. the second position for hundredths. the third for thousandths. then ten-thousandths, hundred-thousandths, millionths, ...
so, you would need 1000 thousandths to have a 1 at the first position before the decimal point. everything less than that has to be a number after the decimal point. and thousandths have to end (writing from left to right) with the thousandths-position. hundredths with the hundredths-position and so on.
If two cards are randomly selected, what is the probability of drawing any one suit first, followed by drawing a face card
Answers
Answer:
0.0181 = 1.81% probability of drawing a suit first, and then a face card.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Probability of drawing a suit first:
4 out of 52 cards are suits, so:
[tex]P(A) = \frac{4}{52} = \frac{1}{13}[/tex]
Followed by drawing a face card:
Considering a suit was drawn, there will be 12 faces in the 51 remaining cards. So
[tex]P(B|A) = \frac{12}{51}[/tex]
What is the probability of drawing a suit first, followed by drawing a face card?
[tex]P(A \cap B) = P(A) \times P(B|A) = \frac{1}{13} \times \frac{12}{51} = \frac{12}{13*51} = 0.0181[/tex]
0.0181 = 1.81% probability of drawing a suit first, and then a face card.
PLEASE HELP ASAP WILL GIVE BRAINLEIST FOR AN ACTUAL ANSWER
Answers
Answer:
<V = 40
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
20x = 60+7x+5
Combine like terms
20x = 7x+65
Subtract 7x from each side
20x -7x = 7x+65-7x
13x = 65
Divide each side by 13
13x/13 = 65/13
x = 5
<v = 7x+5 = 7*5+5 = 35+5 = 40
answer:
it's U = 60°
V = 50°
T = 70°
Suppose you receive the following ANOVA output in this study. What is the correct conclusion about this data (in correct APA format)?
ANOVA
Time Sum of df Mean Square F Sig. Squares Between Groups 91.467 2 45.733 4.467 021 Within 276.400 27 10.237 Groups Total 367.867 29
a. The effect of training on how long it takes to solve the problem was significant, F(2, 27)- 4.47, p> 05.
b. The effect of training on how long it takes to solve the problem was significant, F(2, 27) -4,47, p .05.
c. The effect of training on how long it takes to solve the problem was not significant, F(27, 2)-4.47, p >.05.
d. The effect of training on how long it takes to solve the problem was significant, F(2, 29) - 4.47. p ,05.
Answers
Answer:
The answer is "Option b"
Step-by-step explanation:
Through this context, it is determined that the p-value is much less than 0.05, which is 0.021, so the rejection of the null hypothesis at 5%. There should be enough evidence to demonstrate that now the effect of the organization was substantial on how long it has taken to solve the issue. This result is statistically important.
The correct conclusion about this data is (b) The effect of training on how long it takes to solve the problem was significant, F(2, 27) = 4.47, p < 05.
From the table, we have the following values
F = 4.467
df between group = 2
df within group = 27
To reference the result, we make use of:
F(df between group, df within group) = F value
So, we have:
F(2, 27) = 4.47
The above result shows the F value approximated to two decimal points
Hence, the correct conclusion about this data is (b) The effect of training on how long it takes to solve the problem was significant, F(2, 27) = 4.47, p < 05.
Read more about APA styles at:
https://brainly.com/question/858964
The local pavilion is hosting an outdoor concert. There are both lawn seats and reserved seating available. Lawn seats cost
$10, while reserved seats are $25. A sponsoring business has given the school $375 to purchase seats. If the school
purchased 30 seats using all of the money, how many lawn seats and how many reserved seats did the sponsoring business
purchase?
The business purchased ____ lawn seats and _______ reserved seats
Answers
Let the lawn seats purchased by the business be : L
Let the reserved seats purchased by the business be : R
Given :
⊕ Cost of each lawn seat : $10
⊕ Cost of each reserved seat : $25
⊕ Sponsoring business has given the $375 to purchase seats
⊕ School purchased 30 seats using all of the money
⇒ L + R = 30 ---------- (1)
⇒ 10L + 25R = 375 ----------- (2)
Multiplying equation (1) with 10, we get :
⇒ 10L + 10R = 300 ------------- (3)
Subtracting equation (3) from equation (2), we get :
⇒ 10L + 25R - (10L - 10R) = 375 - 300
⇒ 25R - 10R = 75
⇒ 15R = 75
⇒ R = 5
Substituting R = 5 in equation (1), we get :
⇒ L + 5 = 30
⇒ L = 25
Answer: The Business purchased 25 lawn seats and 5 reserved seats
cu ochii iesiti din orbite propozitie dau coroana
Answers
Answer:
idfk lol hehe hope this helps
Step-by-step explanation:
What is the minimum value of the absolute value parent function on
-10 SX< 10?
Answers
If the first hill is 20 cm high, the second hill is 0 cm high, and the last hill is 0 cm high, how long does it take the 50 g car to reach the egg?
Answers
A sample of 2,000 was sought to estimate the average achievement in science of fifth graders in a city’s public schools. The average fifth grade enrollment in the city’s elementary schools is 100 students. Thus, 20 schools were randomly selected and within each of those schools all fifth graders were tested. What sampling technique was used?
Answers
Answer:
"Clustering sampling" is the correct answer.
Step-by-step explanation:
If our entire demographic has been separated into segments or groupings, people employ clustering sampling. Those same groupings constitute diverse structurally and therefore are necessarily the same thing uniform.Researchers choose certain of the globular groupings, which are taken throughout the sampling one for each of the specified cluster centers.Mrs. Miller claims that 10% of the marbles in the jar are purple. Do the students have statistically significant evidence that the true proportion of purple marbles in the jar is greater than 10%? Use the sampling distribution to help answer the question.
Answers
Answer: C: Yes
Step-by-step explanation:
C on edge 2021
Answer:
The answer is C: Yes, p hat = 0.22 or greater only occurred in 1% of samples in the simulation. Because this is less than 5%, they have statistically significant evidence that the true proportion of purple marbles in the jar is greater than 10%.
Step-by-step explanation:
I just did it.
Using the image above, set up the equation that would help to determine the value
of angle x.
Answers
Answer:
the equation is sin−1 (8/11)
A retail brand plans to open its stores across all cities with a population of more than one million. To prepare for this, it refers to the past year's census done by the government.
Which statement accurately describes the type of data the retail brand is using?
A. The retail brand is relying on raw data because it has to ask for permission to use the census.
B. The retail brand is relying on available data because customers provide information to the census.
C. The census is an example of available data because the government provides it.
D. The census is an example of raw data because the government provides it.
Answers
Answer: C. The census is an example of available data because the government provides it.
Step-by-step explanation:
The statement that accurately describes the type of data the retail brand is using is that census is an example of available data because the government provides it.
Acensus is referred to as an official survey of a country's population which is done in order to know the number of people living there and to know the details of the people like their ages, gender etc.
Draw a negative linear relationship. Label it R. Along a curve showing a linear relationship, how does y change for each increase in x of one unit? For each increase in x of one unit, y _______.
Answers
Answer:
For each unit increase in x ; y decreases by 2 units.
Step-by-step explanation:
A negative relationship between two variables, X and Y is depicted d on a scatter plot by a negative trend line or slope. A negative relationship is interpreted as the decrease in variable X as Y increases or vice versa.
The scatter plot attached is related by the linear model :
y = - 2x + 110
Here, the slope of the plot is - 2 ; this means that for every unit increase in x - axis, then the y values decrease by 2 units.
4(m + 3) = 18
write the solution to the equation
Answers
Answer:
1.5
Step-by-step explanation:
Let's begin by dividing each side by 4.
You get 18/4 or 4.5.
m+3=4.5
Now subtract 3 to each side.
m=1.5
Answer:
[tex]4(m + 3) = 18 \\ 2(m + 3) = 9 \\ 2m + 6 = 9 \\ 2m = 3 \\ m = \frac{3}{2} \\ m = 1.5[/tex]
hich is the graph of the linear equation x – 2y = 6?
On a coordinate plane, a line goes through points (negative 6, 0) and (0, 3).
On a coordinate plane, a line goes through points (0, negative 3) and (6, 0).
On a coordinate plane, a line goes through points (negative 6, 0) and (0, negative 3).
On a coordinate plane, a line goes through points (0, 3) and (6, 0).
Answers
Answer:
B or graph 2
Step-by-step explanation:
when y = 0 then x = 6
when x = 0 then y = -3
find those points
Answer: b
question
hich is the graph of the linear equation x – 2y = 6?
On a coordinate plane, a line goes through points (negative 6, 0) and (0, 3).
On a coordinate plane, a line goes through points (0, negative 3) and (6, 0).
On a coordinate plane, a line goes through points (negative 6, 0) and (0, negative 3).
On a coordinate plane, a line goes through points (0, 3) and (6, 0).
find the difference of the value of the two 6's in the number 6060 ?
Answers
Answer:
5940
Step-by-step explanation:
The first '6' represents '6000' and the second represents '60.'
Thus the difference of the values of the two '6s' is 6000 - 60 = 5940.
In exponential smoothing, the equation involves what type of value that is not part of the moving averages equation?
a. Upper limit
b. Lower limit
c. Level smoothing constant
d. Recent observed value
Answers
Answer:
d. Recent observed value
Step-by-step explanation:
Exponential smoothing is technique for smoothing time series data. In exponential smoothing more recent observed values give larger weights while the weights will decline if observed values are more distant. In moving average the observations were weighted equally.
Explain why in a drawer containing only two different colors of socks one must draw only three socks to find a matching pair
Answers
However there is a probability that if u only pick 2 socks, then they could kid each have different COLORS.
By picking 3 socks (bearing in mind there are only 2 types of color) it’s guaranteed that two socks will have the same color.
PLEASE HELP !!!! WILL MARK BRAINLIEST
Answers
Profit = Revenue - Cost: P = R - C
(a) Solve for R.
(b) Find R when P = $4525 and C = $1475.
Answers
Answer:
(a) R = P +C
Revenue= Profit + Cost
(b) R = $6000
Step-by-step explanation:
(b) R = $4525 + $1475
= $6000
what would be the integer for this problem
???+-8=-2
Answers
Answer:10
Step-by-step explanation:
10 because 10 minus 8 would be 2
Or 6-8= -2
Select all that apply.
There are 3 red marbles, 5 green marbles, and 2 blue marbles in a bag. Which of the following are true?
The probability of randomly drawing a red marble and then a green marble is .
The probability of drawing a green marble is the same as the probability of drawing either a red or a blue marble.
The probability of randomly drawing either a red marble or a green marble is 80%.
The probability of not drawing a blue marble is 20%.
Answers
Step-by-step explanation:
If there are 3 red marbles, 5 green marbles, and 2 blue marbles, we can find the probability of finding one of them easily.
1. If we add these numbers up, we get 10, so the red marbles plus the green marbles = 8 and then there are 2 blue ones. This means that there is an 80% chance of pulling a red or a green marble. Number one is correct.
2. The probability of drawing a red marble followed by a green marble depends on each individual probability. For a red marble, that is [tex]\frac{3}{10}[/tex] = 30% chance, and a green marble is [tex]\frac{5}{10}[/tex] = 50% chance. Since we are drawing out of 20 marbles (Two sets of ten), we can conclude that the chances for red are [tex]\frac{6}{20}[/tex]; green's chances are [tex]\frac{10}{20}[/tex], and blue's chances are [tex]\frac{4}{20}[/tex]. Assuming that we draw a red marble first, there is a [tex]\frac{6}{20}[/tex] chance of that. There is a [tex]\frac{10}{20}[/tex] chance of drawing a green, so we can conclude that the probability of drawing a red marble followed by a green marble is [tex]\frac{4}{20}[/tex] ([tex]\frac{10}{20}[/tex] - [tex]\frac{6}{20}[/tex]), witch is not [tex]\frac{1}{6}[/tex]. Number two is incorrect .
3. The probability of drawing a blue marble is 20%, so the probability of not drawing a blue marble is 80%. Number three is incorrect.
4. The probability of drawing a green marble is 50% and the probabilities of red and blue combined are equal to 50% (3 red + 2 blue = 5, and their are 5 green marbles therefore 50 50 chance). Number four is correct.
Answer:
The probability of randomly drawing a red marble(red 3) and then a green (green 5) marble is [tex]\frac{1}{6}[/tex] .
The probability of drawing a green marble is the same as the probability of drawing either a red or a blue marble.
The probability of randomly drawing either a red marble or a green marble is 80%.
Diameter 24.8 what is radius
Answers
Answer:
12.4
Step-by-step explanation:
to get radius divide diameter by 2
4) Suppose you want to buy a car that costs $11,800. The expected depreciation of the car is 35% per year.
* What percentage is the car worth each year it depreciates from the previous year?
b. Find the depreciated value of the car after 6 years.
Show work please!!!!
Answers
Answer:
$889.94 after six years
Step-by-step explanation:
The equation is I=P(1-r)^t so after six years it would be worth $889.94. Every year the value depreciates by $4,130.
The graph shows the function f(x) = 3^x what is the value of x when f(x) =9
Answers
Answer:
2
Step-by-step explanation:
Substitute 9 in for f(x),
9 = 3ˣ
x = 2.
800 3. Andrew is buying a farm and needs to determine the height of a tree on the farm. Andrew, who is 5.8 feet tall, notices that when his shadow is 10 feet long, the shadow of the tree is 85 feet long. How tall is the tree? (5 points)
Answers
9514 1404 393
Answer:
49.3 feet
Step-by-step explanation:
Shadow lengths and object heights are considered to be proportional, so we have ...
tree height/(tree shadow) = Andrew's height/(Andrew's shadow)
height / (85 ft) = (5.8 ft)/(10 ft)
height = (85 ft)(5.8/10) = 49.3 ft
The tree is 49.3 feet tall.
A brand of uncooked spaghetti comes in a box that is a rectangular prism with a length of 9 inches, a width of 3 inches, and a height of 3 1/2
inches. What is the surface area?
Answers
Answer:
[tex]Area = 138in^2[/tex]
Step-by-step explanation:
Given
[tex]L = 9; W =3; H =3\frac{1}{2}[/tex]
Required
The surface area
This is calculated as:
[tex]Area = 2(LW + LH + WH)[/tex]
So:
[tex]Area = 2(9*3 + 9*3\frac{1}{2} + 3*3\frac{1}{2})[/tex]
[tex]Area = 2(27 + 31\frac{1}{2} + 10\frac{1}{2})[/tex]
[tex]Area = 2*69[/tex]
[tex]Area = 138in^2[/tex]
What is a reasonable estimate for the area of a circle with radius 4cm?
Answers
Answer:
Option D
Explanation:
The real answer would be a bit higher if you use the formula:
Area=π×r^2
A license plate begins with three letters. If the possible letters are A, B, C, D and E, how many different permutations of these letters can be made if no letter is used more than once?
Answers
Answer:
60 different permutations of these letters can be made.
Step-by-step explanation:
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
How many different permutations of these letters can be made if no letter is used more than once?
3 letters from a set of 5. So
[tex]P_{(5,3)} = \frac{5!}{(5-3)!} = \frac{5!}{2!} = 5*4*3 = 60[/tex]
60 different permutations of these letters can be made.
Given the equation of the circle what is the radius? (x-9)2+ (y+5)2 = 36
Answers
Answer:
6
Step-by-step explanation:
In a circle equation, the radius can be found by taking the square root of the r² value.
In this equation, the r² value is 36.
Take the square root:
√36
= 6
So, the radius is 6.